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  4. A block of mass m is connected to three springs as shown in the figure. The block is displaced down slightly and left free, it starts oscillating. Find the time period of oscillations (neglecting gravity). (m=π2 kg ; π2=10 ; θ=60° ; k1=4 N / m ; k2=23 N / m )

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Q. A block of mass $m$ is connected to three springs as shown in the figure. The block is displaced down slightly and left free, it starts oscillating. Find the time period of oscillations (neglecting gravity).
$\left(m=\pi^{2} kg ; \pi^{2}=10 ; \theta=60^{\circ} ; k_{1}=4\, N / m ; k_{2}=23\, N / m \right)$Physics Question Image

Oscillations

Solution:

image
at $GP$
$F_{\text {restoring }}=2 k_{1} x \cos ^{2} \theta +k_{2} x$
So, $T=2 \pi \sqrt{\frac{m}{2 k_{1} \cos ^{2} \theta +k_{2}}}$